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Hydraulic pump: flow, torque and motor power

How much flow does the pump give, and what size motor should it have?

Answer: When a hydraulic pump for a winch, a crane or a steering gear needs to be changed or faulted, you should be able to work out the flow from the pump's swept volume and rev count, and the power the motor should deliver at working pressure. If the flow in practice is far below what's calculated, the pump is worn.

Formula

Flow Q = Vg × n × ηv / 1.000 (l/min, Vg i cm³)

Hydraulisk effekt = p × Q / 600 (kW, p i bar, Q i l/min)

Motoreffekt = hydraulisk effekt / ηt

Moment T = Vg × p / (20π × ηmh), hvor den mekanisk-hydrauliske virkningsgrad ηmh = ηt / ηv

Symbols and units in the formula
SymbolMeaningUnit
vgPump's swept volume (nameplate)cm³/omdr
nRotation speedo/min
eta_vVolumetric efficiency%
pWorking pressurebar
eta_tTotal efficiency%
=Flow from pumpl/min
=Required motor powerkW
=Hydraulic power in the oilkW
=Theoretical flow (without leakage)l/min
=Torque on pump shaftNm

Validity and source

Source
Bosch Rexroth-formler for hydraulikpumper: Q = Vg · n · ηv / 1.000, P = p · Q / 600 / ηt · fagbilag: hydraulikanlæg og pumpetyper

Does not apply when

  • Efficiencies are in the pump's data sheet and depend on pressure, revolutions and oil temperature. A worn pump first loses volumetric efficiency: flow drops, especially at high pressure. Measure flow with a flow meter at working pressure to assess the pump.

Worked example

The calculator's own default values inserted. The figures are calculated with exactly the formula the tool uses.

Substituted

  • Pump's swept volume (nameplate)28 cm³/omdr
  • Rotation speed1,500 o/min
  • Volumetric efficiency95 %
  • Working pressure180 bar
  • Total efficiency85 %

Giver

  • Flow from pump39.9 l/min
  • Required motor power14.1 kW
  • Hydraulic power in the oil12.0 kW
  • Theoretical flow (without leakage)42.0 l/min
  • Torque on pump shaft89.7 Nm

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Sådan bruger du den

Når et hydraulisk spil eller en kran bliver langsom, eller når en pumpe skal skiftes, skal du kende det flow, pumpen bør give, og den motoreffekt, den kræver. Beregneren regner flow, moment og effekt ud fra pumpens slagvolumen, omdrejningstal og arbejdstryk.

Step by step

  1. Aflæs pumpens slagvolumen i cm³ pr. omdrejning på typeskiltet.
  2. Indtast omdrejningstallet for drivmotoren.
  3. Indtast arbejdstrykket og virkningsgraderne fra databladet.
  4. Sammenlign det beregnede flow med det, en flowmåler viser ved samme tryk.

Typical errors

  • At glemme virkningsgraderne. Motoren skal levere mere, end olien får.
  • At måle flowet uden tryk. En slidt pumpe ser fin ud i tomgang.
  • At blande cm³ og liter.
  • At øge omdrejningstallet over pumpens grænse for at få mere flow. Det kan give kavitation.

Examples from everyday life

Pumpe til et ankerspil

Ankerspillets pumpe har 28 cm³/omdr og drives af en 4-polet elmotor på 1.500 o/min. Systemet kører 180 bar.

Pump's swept volume (nameplate)
28 cm³/omdr
Rotation speed
1,500 rpm
Volumetric efficiency
95 %
Working pressure
180 bar
Total efficiency
85 %

It means: Pumpen giver ca. 39.9 l/min, og motoren skal levere ca. 14.1 kW. Pumpeakslen skal have ca. 89.7 Nm.

Slidt pumpe

Spillet er blevet langsomt. Du regner med, at den volumetriske virkningsgrad er faldet til 80 %.

Pump's swept volume (nameplate)
28 cm³/omdr
Rotation speed
1,500 rpm
Volumetric efficiency
80 %
Working pressure
180 bar
Total efficiency
72 %

It means: Flowet falder til 33.6 l/min mod 42 l/min teoretisk. Viser flowmåleren omtrent dette ved arbejdstryk, er pumpen slidt og skal skiftes.

Pumpe til en dækskran

Dækskranens pumpe har 71 cm³/omdr ved 1.800 o/min og 250 bar, med 95 % volumetrisk og 88 % total virkningsgrad.

Pump's swept volume (nameplate)
71 cm³/omdr
Rotation speed
1,800 rpm
Volumetric efficiency
95 %
Working pressure
250 bar
Total efficiency
88 %

It means: Pumpen leverer ca. 121.4 l/min, og motoren skal levere ca. 57.5 kW.

Rule of thumb

kW = bar × l/min / 600. 100 bar og 60 l/min er 10 kW i olien.

How to check the answer

Dobbelt omdrejningstal giver dobbelt flow. Dobbelt tryk giver dobbelt effekt ved samme flow.